1/3 = 0.3333... this is only an approximation because it will never be equal.And.999...9 is always .000...1 short of 1. So it will never be equal to 1.If you think about it, with .999...9 we are specifying that the last digit has to be a 9 which means that it has to be .000...1 short of 1. But, .000...1 approaches 0, but it never actually equals zero because we specifically state that the last digit has to equal a 1. So fundamentally it has to be greater than zero, because if the last digit is always a 1 then the number is always greater than zero, including when we approach zero. I settled the debate lol.
>>16825771That's only if you do it the stupid way by adding.1 - 0.9... = 0.0... "because we specifically state the last digit has to equal 0" lol rekt
The notation $0.99\ldots 9$ doesn't exist in formal mathematics. There is $0.\bar 9$, which is the sum of the infinite series $0.9 + 0.09 + 0.009 + \dots$. Nothing about "the last digit makes any sense.
Despite popular abuses of notation, 0.333... and 0.999... are NOT defined as the result of performing an infinite number of addition operations. Pic related is one way to define them. Another way is the smallest number at least as large as every finite truncation of the decimal.
>>16825796
1/3 = 3/10 + 1/30= 0.3 + 1/30= 0.33 + 1/300= 0.333 + 1/3000:= 0.333... + 1/inf= 0.333... + 0= 0.333...
>>16825771In math, you have to define equality of objects. You yourself have not define what it means to be equal, so there isn't much "real" argument to what you're saying. But it's a legit and reasonable concern, which is why they created these definitions in the first place - to give it a firmer foundation. It's also why you learn about stuff like equivalence classes and shit early on.In math, when they say those two objects are equal, it's more like they are equal because equal is defined for those objects when your "approximation" can get as arbitrarily precise as you want.
The 0.999 schizo midwits are so easy to spot because their entire spiel is>I don't know what a basis is>I was taught decimal and this funny number looks funny in decimal therefore maths is WRONG
>>16826188>math is about precision and exactness>except the abstract numerical identity has non-unique representations in decimal>these non-unique representations are as different as possible>you're a schizo retard if you don't buy in to thisjust like the axioms of infinity and choice, this notion of non-unique number representations is the true schizo perspective. >but muh heckin' formalism who the fuck cares?
>>16825771WAHOO
>>16826222>I don't know what a basis is>I was taught decimal and this funny number looks funny in decimal therefore maths is WRONG
>>16825771The (...) at the end implies infinite repetition of the digit 3 in lower and lower place values, so it is actually equal to 1/3.
>>16825771>.999...9 is always .000...1 short of 1. So it will never be equal to 1.The explicit point of infinity is that this ...1 never occurs, so it is exactly equal to 1. Infinity is not just a very large number, it is something without end.
Finitist>i don't believe in limits and infinity>therefore 0.999... doesn't exist in the first placeSchizophrenic>i don't believe in limits and infinity>but 0.999... exists AND is different than 1 because there is a magical 0.000...001 difference at the end
>>16826599kek
>>16826599>>16826581If 0.000...1 is equal to 0 then why would you even write 0.000...1? What's the point of specifying that there's a 1 at the end if it never occurs? Wouldn't 0.000...1 be an impossibility then? You just can't think abstract like I can. You are not able to imagine the scenario in your head properly.You need to think outside the box a little bit. Imagine a number that has infinite zeroes and THEN a 1. Otherwise 0.000...1 what is it saying if not for that? In that scenario, .999...9 is always less than 1. Perhaps you don't understand infinity.Let me explain. Are there infinite numbers? Yes.Is .999 less than one? Yes. Is .9999 less than one? Yes. Is .99999 less than one? Yes. Can we repeat this pattern forever always adding another 9 at the right? Yes. Will it ever equal one? No. Because it will always end in 9. Lol.
>>16826599>Finitist>therefore 0.999... doesn't existOf course it exists. Finitist 0.999... means as many nines as you need to compare two decimals or to finish an operation or, strictly, as many as the "universe" can "hold" or a human can list out before dying or some such thing.Either way, it's always equal to 1, else the additive identity fails.
